Generalized Linear Mixed Model Approach to Time-to-Event Data with Censored Observations

The time-to-event response is commonly thought of as survival analysis, and typically concerns statistical modeling of expected life span. In the example presented here, alfalfa leafcutting bees, Megachile rotundata, were randomly exposed to one of eight experimental thermoprofiles or two control thermoprofiles, for one to eight weeks. The incorporation of these fluctuating thermoprofiles in the management of the bees increases survival and blocks the development of sub-lethal effects, such as delayed emergence. The data collected here investigates the question of whether any experimental thermoprofile provides better overall survival, with a reduction of sub-lethal effects. The study design incorporates typical aspects of agricultural research; random blocking effects. All M. rotundata prepupae brood cells were randomly placed in individual wells of 24-well culture plates. Plates were randomly assigned to thermoprofile and exposure duration, with three plate replicates per thermoprofile x exposure time. Bees were observed for emergence for 50 days. All bees that were not yet emerged prior to fixed end of study were considered to be censored observations. We fit a generalized linear mixed model (GLMM), using the SAS® GLIMMIX Procedure to the censored data and obtained time-to-emergence function estimates. As opposed to a typical survival analysis approach, such as Kaplan-Meier curve, in the GLMM we were able to include the random model effects from the study design. This is an important inclusion in the model, such that correct standard error and test statistics are generated for mixed models with non-Gaussian data.